def get_kernel_inverse( X_train: np.ndarray, hyps: dict, str_cov: str, fix_noise: bool = constants.FIX_GP_NOISE, use_gradient: bool = False, debug: bool = False) -> constants.TYPING_TUPLE_THREE_ARRAYS: """ This function computes a kernel inverse without any matrix decomposition techniques. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param hyps: dictionary of hyperparameters for Gaussian process. :type hyps: dict. :param str_cov: the name of covariance function. :type str_cov: str. :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param use_gradient: flag for computing and returning gradients of negative log marginal likelihood. :type use_gradient: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of kernel matrix over `X_train`, kernel matrix inverse, and gradients of kernel matrix. If `use_gradient` is False, gradients of kernel matrix would be None. :rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray) :raises: AssertionError """ assert isinstance(X_train, np.ndarray) assert isinstance(hyps, dict) assert isinstance(str_cov, str) assert isinstance(use_gradient, bool) assert isinstance(fix_noise, bool) assert isinstance(debug, bool) utils_covariance.check_str_cov('get_kernel_inverse', str_cov, X_train.shape) cov_X_X = cov_main(str_cov, X_train, X_train, hyps, True) \ + hyps['noise']**2 * np.eye(X_train.shape[0]) cov_X_X = (cov_X_X + cov_X_X.T) / 2.0 inv_cov_X_X = np.linalg.inv(cov_X_X) if use_gradient: grad_cov_X_X = grad_cov_main(str_cov, X_train, X_train, hyps, fix_noise, same_X_Xp=True) else: grad_cov_X_X = None return cov_X_X, inv_cov_X_X, grad_cov_X_X
def predict_with_cov(X_train: np.ndarray, Y_train: np.ndarray, X_test: np.ndarray, cov_X_X: np.ndarray, inv_cov_X_X: np.ndarray, hyps: dict, str_cov: str=constants.STR_COV, prior_mu: constants.TYPING_UNION_CALLABLE_NONE=None, debug: bool=False ) -> constants.TYPING_TUPLE_THREE_ARRAYS: """ This function returns posterior mean and posterior standard deviation functions over `X_test`, computed by Gaussian process regression with `X_train`, `Y_train`, `cov_X_X`, `inv_cov_X_X`, and `hyps`. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param X_test: inputs. Shape: (l, d) or (l, m, d). :type X_test: numpy.ndarray :param cov_X_X: kernel matrix over `X_train`. Shape: (n, n). :type cov_X_X: numpy.ndarray :param inv_cov_X_X: kernel matrix inverse over `X_train`. Shape: (n, n). :type inv_cov_X_X: numpy.ndarray :param hyps: dictionary of hyperparameters for Gaussian process. :type hyps: dict. :param str_cov: the name of covariance function. :type str_cov: str., optional :param prior_mu: None, or prior mean function. :type prior_mu: NoneType, or callable, optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of posterior mean function over `X_test`, posterior standard deviation function over `X_test`, and posterior covariance matrix over `X_test`. Shape: ((l, 1), (l, 1), (l, l)). :rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray) :raises: AssertionError """ utils_gp.validate_common_args(X_train, Y_train, str_cov, prior_mu, debug, X_test) assert isinstance(cov_X_X, np.ndarray) assert isinstance(inv_cov_X_X, np.ndarray) assert isinstance(hyps, dict) assert len(cov_X_X.shape) == 2 assert len(inv_cov_X_X.shape) == 2 assert (np.array(cov_X_X.shape) == np.array(inv_cov_X_X.shape)).all() utils_covariance.check_str_cov('predict_with_cov', str_cov, X_train.shape, shape_X2=X_test.shape) prior_mu_train = utils_gp.get_prior_mu(prior_mu, X_train) prior_mu_test = utils_gp.get_prior_mu(prior_mu, X_test) cov_X_Xs = covariance.cov_main(str_cov, X_train, X_test, hyps, False) cov_Xs_Xs = covariance.cov_main(str_cov, X_test, X_test, hyps, True) cov_Xs_Xs = (cov_Xs_Xs + cov_Xs_Xs.T) / 2.0 mu_Xs = np.dot(np.dot(cov_X_Xs.T, inv_cov_X_X), Y_train - prior_mu_train) + prior_mu_test Sigma_Xs = cov_Xs_Xs - np.dot(np.dot(cov_X_Xs.T, inv_cov_X_X), cov_X_Xs) return mu_Xs, np.expand_dims(np.sqrt(np.maximum(np.diag(Sigma_Xs), 0.0)), axis=1), Sigma_Xs
def predict_with_optimized_hyps(X_train: np.ndarray, Y_train: np.ndarray, X_test: np.ndarray, str_cov: str=constants.STR_COV, str_optimizer_method: str=constants.STR_OPTIMIZER_METHOD_GP, prior_mu: constants.TYPING_UNION_CALLABLE_NONE=None, fix_noise: float=constants.FIX_GP_NOISE, debug: bool=False ) -> constants.TYPING_TUPLE_THREE_ARRAYS: """ This function returns posterior mean and posterior standard deviation functions over `X_test`, computed by the Gaussian process regression optimized with `X_train` and `Y_train`. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param X_test: inputs. Shape: (l, d) or (l, m, d). :type X_test: numpy.ndarray :param str_cov: the name of covariance function. :type str_cov: str., optional :param str_optimizer_method: the name of optimization method. :type str_optimizer_method: str., optional :param prior_mu: None, or prior mean function. :type prior_mu: NoneType, or callable, optional :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of posterior mean function over `X_test`, posterior standard deviation function over `X_test`, and posterior covariance matrix over `X_test`. Shape: ((l, 1), (l, 1), (l, l)). :rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray) :raises: AssertionError """ utils_gp.validate_common_args(X_train, Y_train, str_cov, prior_mu, debug, X_test) assert isinstance(str_optimizer_method, str) assert isinstance(fix_noise, bool) utils_covariance.check_str_cov('predict_with_optimized_kernel', str_cov, X_train.shape, shape_X2=X_test.shape) assert str_optimizer_method in constants.ALLOWED_OPTIMIZER_METHOD_GP time_start = time.time() cov_X_X, inv_cov_X_X, hyps = gp_kernel.get_optimized_kernel(X_train, Y_train, prior_mu, str_cov, str_optimizer_method=str_optimizer_method, fix_noise=fix_noise, debug=debug) mu_Xs, sigma_Xs, Sigma_Xs = predict_with_cov(X_train, Y_train, X_test, cov_X_X, inv_cov_X_X, hyps, str_cov=str_cov, prior_mu=prior_mu, debug=debug) time_end = time.time() if debug: logger.debug('time consumed to construct gpr: %.4f sec.', time_end - time_start) return mu_Xs, sigma_Xs, Sigma_Xs
def predict_with_hyps(X_train: np.ndarray, Y_train: np.ndarray, X_test: np.ndarray, hyps: dict, str_cov: str=constants.STR_COV, prior_mu: constants.TYPING_UNION_CALLABLE_NONE=None, debug: bool=False ) -> constants.TYPING_TUPLE_THREE_ARRAYS: """ This function returns posterior mean and posterior standard deviation functions over `X_test`, computed by Gaussian process regression with `X_train`, `Y_train`, and `hyps`. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param X_test: inputs. Shape: (l, d) or (l, m, d). :type X_test: numpy.ndarray :param hyps: dictionary of hyperparameters for Gaussian process. :type hyps: dict. :param str_cov: the name of covariance function. :type str_cov: str., optional :param prior_mu: None, or prior mean function. :type prior_mu: NoneType, or callable, optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of posterior mean function over `X_test`, posterior standard deviation function over `X_test`, and posterior covariance matrix over `X_test`. Shape: ((l, 1), (l, 1), (l, l)). :rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray) :raises: AssertionError """ utils_gp.validate_common_args(X_train, Y_train, str_cov, prior_mu, debug, X_test) assert isinstance(hyps, dict) utils_covariance.check_str_cov('predict_with_hyps', str_cov, X_train.shape, shape_X2=X_test.shape) cov_X_X, inv_cov_X_X, _ = covariance.get_kernel_inverse(X_train, hyps, str_cov, debug=debug) mu_Xs, sigma_Xs, Sigma_Xs = predict_with_cov(X_train, Y_train, X_test, cov_X_X, inv_cov_X_X, hyps, str_cov=str_cov, prior_mu=prior_mu, debug=debug) return mu_Xs, sigma_Xs, Sigma_Xs
def get_optimized_kernel( X_train: np.ndarray, Y_train: np.ndarray, prior_mu: constants.TYPING_UNION_CALLABLE_NONE, str_cov: str, str_optimizer_method: str = constants.STR_OPTIMIZER_METHOD_GP, str_modelselection_method: str = constants.STR_MODELSELECTION_METHOD, use_ard: bool = constants.USE_ARD, fix_noise: bool = constants.FIX_GP_NOISE, debug: bool = False) -> constants.TYPING_TUPLE_TWO_ARRAYS_DICT: """ This function computes the kernel matrix optimized by optimization method specified, its inverse matrix, and the optimized hyperparameters. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param prior_mu: prior mean function or None. :type prior_mu: callable or NoneType :param str_cov: the name of covariance function. :type str_cov: str. :param str_optimizer_method: the name of optimization method. :type str_optimizer_method: str., optional :param str_modelselection_method: the name of model selection method. :type str_modelselection_method: str., optional :param use_ard: flag for using automatic relevance determination. :type use_ard: bool., optional :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of kernel matrix over `X_train`, kernel matrix inverse, and dictionary of hyperparameters. :rtype: tuple of (numpy.ndarray, numpy.ndarray, dict.) :raises: AssertionError, ValueError """ # TODO: check to input same fix_noise to convert_hyps and restore_hyps utils_gp.validate_common_args(X_train, Y_train, str_cov, prior_mu, debug) assert isinstance(str_optimizer_method, str) assert isinstance(str_modelselection_method, str) assert isinstance(use_ard, bool) assert isinstance(fix_noise, bool) utils_covariance.check_str_cov('get_optimized_kernel', str_cov, X_train.shape) assert str_optimizer_method in constants.ALLOWED_OPTIMIZER_METHOD_GP assert str_modelselection_method in constants.ALLOWED_MODELSELECTION_METHOD use_gradient = bool(str_optimizer_method != 'Nelder-Mead') # TODO: Now, use_gradient is fixed as False. # use_gradient = False time_start = time.time() if debug: logger.debug('str_optimizer_method: %s', str_optimizer_method) logger.debug('str_modelselection_method: %s', str_modelselection_method) logger.debug('use_gradient: %s', use_gradient) prior_mu_train = utils_gp.get_prior_mu(prior_mu, X_train) if str_cov in constants.ALLOWED_COV_BASE: num_dim = X_train.shape[1] elif str_cov in constants.ALLOWED_COV_SET: num_dim = X_train.shape[2] use_gradient = False if str_modelselection_method == 'ml': neg_log_ml_ = lambda hyps: gp_likelihood.neg_log_ml( X_train, Y_train, hyps, str_cov, prior_mu_train, use_ard=use_ard, fix_noise=fix_noise, use_gradient=use_gradient, debug=debug) elif str_modelselection_method == 'loocv': # TODO: add use_ard. neg_log_ml_ = lambda hyps: gp_likelihood.neg_log_pseudo_l_loocv( X_train, Y_train, hyps, str_cov, prior_mu_train, fix_noise=fix_noise, debug=debug) use_gradient = False else: # pragma: no cover raise ValueError( 'get_optimized_kernel: missing conditions for str_modelselection_method.' ) hyps_converted = utils_covariance.convert_hyps(str_cov, utils_covariance.get_hyps( str_cov, num_dim, use_ard=use_ard), fix_noise=fix_noise) if str_optimizer_method in ['BFGS', 'SLSQP']: result_optimized = scipy.optimize.minimize(neg_log_ml_, hyps_converted, method=str_optimizer_method, jac=use_gradient, options={'disp': False}) if debug: logger.debug('negative log marginal likelihood: %.6f', result_optimized.fun) logger.debug('scipy message: %s', result_optimized.message) result_optimized = result_optimized.x elif str_optimizer_method in ['L-BFGS-B', 'SLSQP-Bounded']: if str_optimizer_method == 'SLSQP-Bounded': str_optimizer_method = 'SLSQP' bounds = utils_covariance.get_range_hyps(str_cov, num_dim, use_ard=use_ard, fix_noise=fix_noise) result_optimized = scipy.optimize.minimize(neg_log_ml_, hyps_converted, method=str_optimizer_method, bounds=bounds, jac=use_gradient, options={'disp': False}) if debug: logger.debug('negative log marginal likelihood: %.6f', result_optimized.fun) logger.debug('scipy message: %s', result_optimized.message) result_optimized = result_optimized.x elif str_optimizer_method in ['Nelder-Mead']: result_optimized = scipy.optimize.minimize(neg_log_ml_, hyps_converted, method=str_optimizer_method, options={'disp': False}) if debug: logger.debug('negative log marginal likelihood: %.6f', result_optimized.fun) logger.debug('scipy message: %s', result_optimized.message) result_optimized = result_optimized.x else: # pragma: no cover raise ValueError( 'get_optimized_kernel: missing conditions for str_optimizer_method' ) hyps = utils_covariance.restore_hyps(str_cov, result_optimized, use_ard=use_ard, fix_noise=fix_noise) hyps = utils_covariance.validate_hyps_dict(hyps, str_cov, num_dim) cov_X_X, inv_cov_X_X, _ = covariance.get_kernel_inverse( X_train, hyps, str_cov, fix_noise=fix_noise, debug=debug) time_end = time.time() if debug: logger.debug('hyps optimized: %s', utils_logger.get_str_hyps(hyps)) logger.debug('time consumed to construct gpr: %.4f sec.', time_end - time_start) return cov_X_X, inv_cov_X_X, hyps
def neg_log_ml(X_train: np.ndarray, Y_train: np.ndarray, hyps: np.ndarray, str_cov: str, prior_mu_train: np.ndarray, use_ard: bool = constants.USE_ARD, fix_noise: bool = constants.FIX_GP_NOISE, use_gradient: bool = True, debug: bool = False) -> constants.TYPING_UNION_FLOAT_FA: """ This function computes a negative log marginal likelihood. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param hyps: hyperparameters for Gaussian process. Shape: (h, ). :type hyps: numpy.ndarray :param str_cov: the name of covariance function. :type str_cov: str. :param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1). :type prior_mu_train: numpy.ndarray :param use_ard: flag for automatic relevance determination. :type use_ard: bool., optional :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param use_gradient: flag for computing and returning gradients of negative log marginal likelihood. :type use_gradient: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: negative log marginal likelihood, or (negative log marginal likelihood, gradients of the likelihood). :rtype: float, or tuple of (float, np.ndarray) :raises: AssertionError """ utils_gp.validate_common_args(X_train, Y_train, str_cov, None, debug) assert isinstance(hyps, np.ndarray) assert isinstance(prior_mu_train, np.ndarray) assert isinstance(use_ard, bool) assert isinstance(fix_noise, bool) assert isinstance(use_gradient, bool) assert len(prior_mu_train.shape) == 2 assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0] utils_covariance.check_str_cov('neg_log_ml', str_cov, X_train.shape) num_X = float(X_train.shape[0]) hyps = utils_covariance.restore_hyps(str_cov, hyps, use_ard=use_ard, fix_noise=fix_noise, use_gp=False) new_Y_train = Y_train - prior_mu_train nu = hyps['dof'] cov_X_X, inv_cov_X_X, grad_cov_X_X = covariance.get_kernel_inverse( X_train, hyps, str_cov, fix_noise=fix_noise, use_gradient=use_gradient, debug=debug) alpha = np.dot(inv_cov_X_X, new_Y_train) beta = np.squeeze(np.dot(np.dot(new_Y_train.T, inv_cov_X_X), new_Y_train)) first_term = -0.5 * num_X * np.log((nu - 2.0) * np.pi) sign_second_term, second_term = np.linalg.slogdet(cov_X_X) # TODO: it should be checked. if sign_second_term <= 0: # pragma: no cover second_term = 0.0 second_term = -0.5 * second_term third_term = np.log( scipy.special.gamma( (nu + num_X) / 2.0) / scipy.special.gamma(nu / 2.0)) fourth_term = -0.5 * (nu + num_X) * np.log(1.0 + beta / (nu - 2.0)) log_ml_ = np.squeeze(first_term + second_term + third_term + fourth_term) log_ml_ /= num_X if use_gradient: assert grad_cov_X_X is not None grad_log_ml_ = np.zeros(grad_cov_X_X.shape[2] + 1) first_term_grad = ((nu + num_X) / (nu + beta - 2.0) * np.dot(alpha, alpha.T) - inv_cov_X_X) nu_grad = -num_X / (2.0 * (nu - 2.0))\ + scipy.special.digamma((nu + num_X) / 2.0)\ - scipy.special.digamma(nu / 2.0)\ - 0.5 * np.log(1.0 + beta / (nu - 2.0))\ + (nu + num_X) * beta / (2.0 * (nu - 2.0)**2 + 2.0 * beta * (nu - 2.0)) if fix_noise: grad_log_ml_[0] = nu_grad else: grad_log_ml_[1] = nu_grad for ind in range(0, grad_cov_X_X.shape[2]): cur_grad = 0.5 * np.trace( np.dot(first_term_grad, grad_cov_X_X[:, :, ind])) if fix_noise: grad_log_ml_[ind + 1] = cur_grad else: if ind == 0: cur_ind = 0 else: cur_ind = ind + 1 grad_log_ml_[cur_ind] = cur_grad if use_gradient: return -1.0 * log_ml_, -1.0 * grad_log_ml_ / num_X return -1.0 * log_ml_
def get_kernel_cholesky( X_train: np.ndarray, hyps: dict, str_cov: str, fix_noise: bool = constants.FIX_GP_NOISE, use_gradient: bool = False, debug: bool = False) -> constants.TYPING_TUPLE_THREE_ARRAYS: """ This function computes a kernel inverse with Cholesky decomposition. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param hyps: dictionary of hyperparameters for Gaussian process. :type hyps: dict. :param str_cov: the name of covariance function. :type str_cov: str. :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param use_gradient: flag for computing and returning gradients of negative log marginal likelihood. :type use_gradient: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: a tuple of kernel matrix over `X_train`, lower matrix computed by Cholesky decomposition, and gradients of kernel matrix. If `use_gradient` is False, gradients of kernel matrix would be None. :rtype: tuple of (numpy.ndarray, numpy.ndarray, numpy.ndarray) :raises: AssertionError, ValueError """ assert isinstance(X_train, np.ndarray) assert isinstance(hyps, dict) assert isinstance(str_cov, str) assert isinstance(fix_noise, bool) assert isinstance(use_gradient, bool) assert isinstance(debug, bool) utils_covariance.check_str_cov('get_kernel_cholesky', str_cov, X_train.shape) cov_X_X = cov_main(str_cov, X_train, X_train, hyps, True) \ + hyps['noise']**2 * np.eye(X_train.shape[0]) cov_X_X = (cov_X_X + cov_X_X.T) / 2.0 lower = None for jitter_cov in [0.0, 1e-4, 1e-2, 1e-1, 1e0, 1e1, 1e2]: try: cov_X_X_ = cov_X_X + jitter_cov * np.eye(X_train.shape[0]) lower = scipy.linalg.cholesky(cov_X_X_, lower=True) # TODO: check this. cov_X_X = cov_X_X_ break except np.linalg.LinAlgError: # pragma: no cover pass if lower is None: # pragma: no cover raise ValueError('jitter_cov is not large enough.') if use_gradient: grad_cov_X_X = grad_cov_main(str_cov, X_train, X_train, hyps, fix_noise, same_X_Xp=True) else: grad_cov_X_X = None return cov_X_X, lower, grad_cov_X_X
def neg_log_ml(X_train: np.ndarray, Y_train: np.ndarray, hyps: np.ndarray, str_cov: str, prior_mu_train: np.ndarray, use_ard: bool=constants.USE_ARD, fix_noise: bool=constants.FIX_GP_NOISE, use_cholesky: bool=True, use_gradient: bool=True, debug: bool=False ) -> constants.TYPING_UNION_FLOAT_FA: """ This function computes a negative log marginal likelihood. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param hyps: hyperparameters for Gaussian process. Shape: (h, ). :type hyps: numpy.ndarray :param str_cov: the name of covariance function. :type str_cov: str. :param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1). :type prior_mu_train: numpy.ndarray :param use_ard: flag for automatic relevance determination. :type use_ard: bool., optional :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param use_cholesky: flag for using a cholesky decomposition. :type use_cholesky: bool., optional :param use_gradient: flag for computing and returning gradients of negative log marginal likelihood. :type use_gradient: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: negative log marginal likelihood, or (negative log marginal likelihood, gradients of the likelihood). :rtype: float, or tuple of (float, np.ndarray) :raises: AssertionError """ # TODO: add use_ard. utils_gp.validate_common_args(X_train, Y_train, str_cov, None, debug) assert isinstance(hyps, np.ndarray) assert isinstance(prior_mu_train, np.ndarray) assert isinstance(use_ard, bool) assert isinstance(fix_noise, bool) assert isinstance(use_cholesky, bool) assert isinstance(use_gradient, bool) assert len(prior_mu_train.shape) == 2 assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0] utils_covariance.check_str_cov('neg_log_ml', str_cov, X_train.shape) hyps = utils_covariance.restore_hyps(str_cov, hyps, use_ard=use_ard, fix_noise=fix_noise) new_Y_train = Y_train - prior_mu_train if use_cholesky: cov_X_X, lower, grad_cov_X_X = covariance.get_kernel_cholesky(X_train, hyps, str_cov, fix_noise=fix_noise, use_gradient=use_gradient, debug=debug) alpha = scipy.linalg.cho_solve((lower, True), new_Y_train) first_term = -0.5 * np.dot(new_Y_train.T, alpha) second_term = -1.0 * np.sum(np.log(np.diagonal(lower) + constants.JITTER_LOG)) if use_gradient: assert grad_cov_X_X is not None first_term_grad = np.einsum("ik,jk->ijk", alpha, alpha) first_term_grad -= np.expand_dims(scipy.linalg.cho_solve((lower, True), np.eye(cov_X_X.shape[0])), axis=2) grad_log_ml_ = 0.5 * np.einsum("ijl,ijk->kl", first_term_grad, grad_cov_X_X) grad_log_ml_ = np.sum(grad_log_ml_, axis=1) else: # TODO: use_gradient is fixed. use_gradient = False cov_X_X, inv_cov_X_X, grad_cov_X_X = covariance.get_kernel_inverse(X_train, hyps, str_cov, fix_noise=fix_noise, use_gradient=use_gradient, debug=debug) first_term = -0.5 * np.dot(np.dot(new_Y_train.T, inv_cov_X_X), new_Y_train) sign_second_term, second_term = np.linalg.slogdet(cov_X_X) # TODO: It should be checked. if sign_second_term <= 0: # pragma: no cover second_term = 0.0 second_term = -0.5 * second_term third_term = -float(X_train.shape[0]) / 2.0 * np.log(2.0 * np.pi) log_ml_ = np.squeeze(first_term + second_term + third_term) log_ml_ /= X_train.shape[0] if use_gradient: return -1.0 * log_ml_, -1.0 * grad_log_ml_ / X_train.shape[0] return -1.0 * log_ml_
def neg_log_pseudo_l_loocv(X_train: np.ndarray, Y_train: np.ndarray, hyps: np.ndarray, str_cov: str, prior_mu_train: np.ndarray, fix_noise: bool=constants.FIX_GP_NOISE, debug: bool=False ) -> float: """ It computes a negative log pseudo-likelihood using leave-one-out cross-validation. :param X_train: inputs. Shape: (n, d) or (n, m, d). :type X_train: numpy.ndarray :param Y_train: outputs. Shape: (n, 1). :type Y_train: numpy.ndarray :param hyps: hyperparameters for Gaussian process. Shape: (h, ). :type hyps: numpy.ndarray :param str_cov: the name of covariance function. :type str_cov: str. :param prior_mu_train: the prior values computed by get_prior_mu(). Shape: (n, 1). :type prior_mu_train: numpy.ndarray :param fix_noise: flag for fixing a noise. :type fix_noise: bool., optional :param debug: flag for printing log messages. :type debug: bool., optional :returns: negative log pseudo-likelihood. :rtype: float :raises: AssertionError """ # TODO: add use_ard. utils_gp.validate_common_args(X_train, Y_train, str_cov, None, debug) assert isinstance(hyps, np.ndarray) assert isinstance(prior_mu_train, np.ndarray) assert isinstance(fix_noise, bool) assert len(prior_mu_train.shape) == 2 assert X_train.shape[0] == Y_train.shape[0] == prior_mu_train.shape[0] utils_covariance.check_str_cov('neg_log_pseudo_l_loocv', str_cov, X_train.shape) num_data = X_train.shape[0] hyps = utils_covariance.restore_hyps(str_cov, hyps, fix_noise=fix_noise) _, inv_cov_X_X, _ = covariance.get_kernel_inverse(X_train, hyps, str_cov, fix_noise=fix_noise, debug=debug) log_pseudo_l_ = 0.0 for ind_data in range(0, num_data): # TODO: check this. # cur_X_train = np.vstack((X_train[:ind_data], X_train[ind_data+1:])) # cur_Y_train = np.vstack((Y_train[:ind_data], Y_train[ind_data+1:])) # cur_X_test = np.expand_dims(X_train[ind_data], axis=0) cur_Y_test = Y_train[ind_data] cur_mu = np.squeeze(cur_Y_test) \ - np.dot(inv_cov_X_X, Y_train)[ind_data] / inv_cov_X_X[ind_data, ind_data] cur_sigma = np.sqrt(1.0 / (inv_cov_X_X[ind_data, ind_data] + constants.JITTER_COV)) first_term = -0.5 * np.log(cur_sigma**2) second_term = -0.5 * (np.squeeze(cur_Y_test - cur_mu))**2 / (cur_sigma**2) third_term = -0.5 * np.log(2.0 * np.pi) cur_log_pseudo_l_ = first_term + second_term + third_term log_pseudo_l_ += cur_log_pseudo_l_ log_pseudo_l_ /= num_data log_pseudo_l_ *= -1.0 return log_pseudo_l_
def test_check_str_cov(): with pytest.raises(AssertionError) as error: package_target.check_str_cov(1, 'se', (2, 1)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 1, (2, 1)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'se', 1) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'se', (2, 100, 100)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'se', (2, 100), shape_X2=(2, 100, 100)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'set_se', (2, 100), shape_X2=(2, 100, 100)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'set_se', (2, 100, 100), shape_X2=(2, 100)) with pytest.raises(AssertionError) as error: package_target.check_str_cov('test', 'se', (2, 1), shape_X2=1) with pytest.raises(ValueError) as error: package_target.check_str_cov('test', 'abc', (2, 1))